A multiple choice exam consists of 10 questions, each with only one correct answ

Question

A multiple choice exam consists of 10 questions, each with only one correct answer out of four choices. Find each of the following if Peter randomly guesses at each question. (a) Find the probability that Peter gets exactly three correct. Find the probability that Peter gets less than two correct. Find the mean and standard deviation for the number correct. Would it be unusual for Peter to get five correct? Construct a u+20 interval to answer this question. A bone mineral density test is used to determine a bone disease. The result of a come commonly measured as a z score, and the population of z scores is ne a z score, and the population of z scores is normally distributed with a mean calculate each of the following. (4 decimals) deviation of 1. Use either the standard normal table or your graphing calculator w (a) For a randomly selected subiect find ut a fandomly selected subject, find the probability of a homo da 2.07

Explanation / Answer

n = 10

p = 1/4 = 0.25

This is a binomial distribution

P(X = x) = 10Cx * 0.25x * (1 - 0.25)10-x

a) P(X = 3) = 10C3 * 0.253 * 0.757 = 0.2503

b) P(X < 2) = P(X = 0) + P(X = 1)

                   = 10C0 * 0.250 * 0.7510 + 10C1 * 0.251 * 0.759

                   = 0.2440

c) mean = n * p = 10 * 0.25 = 2.5

sd = sqrt(n * p * (1 - p)) = sqrt(10 * 0.25 * 0.75) = 1.37

d) mean + 2 * sd = 2.5 + 2 * 1.37 = 5.24

It is not unusual, because 5 is less than 5.24

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